Tobit or OLS? An empirical evaluation under different diary window lengths

Researchers analysing time-use data often estimate limited dependent variable models because time spent must be nonnegative and cannot be more than the total amount of time in a given observation period. While the traditional empirical technique applied to such cases is maximum likelihood estimation of a Tobit (censored regression) model, recent debate has questioned whether linear models estimated via Ordinary Least Squares (OLS) are preferable. On the one hand, Tobit models are deemed necessary to address the significant censoring (i.e. large numbers of zeroes) typically found in time-use data, in the face of which OLS estimators would be biased and inconsistent. Yet, optimization occurs over a longer period than that covered by the typical time diary (often a day), and thus some argue that reported zeroes represent a measurement problem rather than true nonparticipation in the activity, in which case OLS would be preferred. We provide direct empirical evidence on this question using the Australian Time Use Surveys, which record time-use information for two consecutive diary days, by estimating censored and linear versions of a parental child care model for both 24-hour and 48-hour windows of observation in order to determine the empirical consequences of estimation technique and diary length.